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COMEDK2024Evening ShiftMathematicsDeterminantsActual

If A= [ array ccc 0 & x & 16 x & 5 & 7 0 & 9 & x array ] is a singular matrix then x is equal to

Options

  1. A-144
  2. B144
  3. C21
  4. D-12

Correct answer

D. -12

Step-by-step solution

For singular matrix, |A| = 0 Expanding along first column (two zeros): |A| = 0 - x vmatrix x & 16 9 & x vmatrix + 0 = -x(x^2 - 144) Setting |A| = 0 : -x(x^2 - 144) = 0 x = 0 or x = 12 Among the given options, x = -12 .

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